A Splitting Theorem for Local Cohomology and its Applications

Let $R$ be a commutative Noetherian ring and $M$ a finitely generated $R$-module. We show in this paper that, for an integer $t$, if the local cohomology module $H^{i}_\mathfrak{a}(M)$ with respect to an ideal $\frak a$ is finitely generated for all $i<t$, then $$H^{i}_\mathfrak{a}(M/xM)\cong H^{i}_\mathfrak{a}(M)\oplus H^{i+1}_\mathfrak{a}(M)$for all$\frak a$-filter regular elements$x$containing in a enough large power of$\frak a$and all$i<t-1$. As consequences we obtain generalizations, by very short proofs, of the main results of M. Brodmann and A.L. Faghani (A finiteness result for associated primes of local cohomology modules, Proc. Amer. Math. Soc., 128(2000), 2851-2853) and of H.L. Truong and the first author (Asymptotic behavior of parameter ideals in generalized Cohen-Macaulay module, J. Algebra, 320(2008),158-168).Comment: to appear in J. Algebr

Existence of competitive equilibrium in a single-sector growth model with heterogeneous agents and endogenous leisure

We prove the existence of competitive equilibrium in a single-sector dynamic economy with heterogeneous agents and elastic labor supply. The method of proof relies on exploiting the existence of Lagrange multipliers in infinite dimensional spaces and the link between Pareto-optima and competitive equilibria.Optimal growth model, Lagrange multipliers, single-sector growth model, competitive equilibrium, elastic labor supply.

Equilibrium dynamics in an aggregative model of capital accumulation with heterogeneous agents and elastic labor

The paper extends the canonical representative agent Ramsey model to include heterogeneous agents and elastic labor supply. The welfare maximization problem is analyzed and shown to be equivalent to a non-stationary reduced form model. An iterative procedure is exploited to prove the supermodularity of the indirect utility function. Supermodularity is subsequently used to establish the convergence of optimal paths.Single-sector growth model, heterogeneous agents, elastic labor supply.

Existence of competitive equilibrium in an optimal growth model with heterogeneous agents and endogenous leisure

This paper proves the existence of competitive equilibrium in a single-sector dynamic economy with heterogeneous agents, elastic labor supply and complete assets markets. The method of proof relies on some recent results concerning the existence of Lagrande multipliers in infinite dimensional spaces and their representation as a summable sequence and a direct application of the inward boundary fixed point theorem.Optimal growth model, Lagrange multipliers, competitive equilibrium, individually rational Pareto Optimum, elastic labor supply.

Non-convex Aggregate Technology and Optimal Economic Growth

This paper examines a model of optimal growth where the aggregation of two separate well behaved and concave production technologies exhibits a basic non-convexity. First, we consider the case of strictly concave utility function: when the discount rate is either low enough or high enough, there will be one steady state equilibrium toward which the convergence of the optimal paths is monotone and asymptotic. When the discount rate is in some intermediate range, we find sufficient conditions for having either one equilibrium or multiple equilibria steady state. Depending to whether the initial capital per capita is located with respect to a critical value, the optimal paths converge to one single appropriate equilibrium steady state. This state might be a poverty trap with low per capita capital, which acts as the extinction state encountered in earlier studies focused on S-shapes production functions. Second, we consider the case of linear utility and provide sufficient conditions to have either unique or two steady states when the discount rate is in some intermediate range . In the latter case, we give conditions under which the above critical value might not exist, and the economy attains one steady state infinite time, then stays at the other steady state afterward.Non-convex agreggative technology - optimal economic growth - steady state

Equilibrium dynamics in an aggregative model of capital accumulation with heterogeneous agents and elastic labor

The paper extends the canonical representative agent Ramsey model to include heterogeneous agents and elastic labor supply. The welfare maximization problem is analyzed and shown to be equivalent to a non-stationary reduced form model. An iterative procedure is exploited to prove the supermodularity of the indirect utility function. Supermodularity is subsequently used to establish the convergence of optimal paths.Single-sector growth model, heterogeneous agents, elastic labor supply, supermodularity